An extended mutation concept for the local selection based differential evolution algorithm

Social learning differential evolution

Differential evolution algorithms represent an efficient framework to solve complicated optimization tasks with many variables and complex constraints. Nevertheless, the classic differential evolution algorithm does not guarantee the convergence to the global minimum of the cost function. Therefore, the authors developed a modification of this algorithm that ensures asymptotic global convergence. The article provides a comparison of the ability to identify the global minimum of the cost function for the following three algorithms: the classic differential evolution algorithm, the above mentioned modified differential evolution algorithm and an algorithm of random sampling enhanced by a hill climbing procedure. We designed a series of numerical experiments to perform this comparison. The results indicate that the classic differential evolution algorithm is in general an extremely poor global optimizer (global minimum found in 2% of cases). On the other hand the performance of the modified differential evol...

t—Differential evolution algorithm in solving complex function optimization problems, the problems of convergence rate and precision is not high. At the same time, there is a big difference in the performance of evolutionary algorithms for solving the different types of optimization problems. To solve above two problems, this paper proposes a dynamic multimodal differential evolution algorithm. Firstly, the dynamically population is used to improve the exploration ability of algorithms; In addition, the algorithm uses Four different types of mutation operator to Produce among individuals, choose the best among individuals to enter the next iteration , improved the algorithms's performance of solving different types of optimization problems. Through a variety of BenchMark functions to the algorithm simulation experiment, and comparing and several other classical differential evolution algorithm, show that this algorithm has better optimization performance. Keywords—Differential evolution, Convergence rate, Mutation Operator 一种动态多模式差分演化算法 董小刚 ,谢清 ,柯林 2 1) 九江学院信息科学与技术学院,九江 江西 中国

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks.In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function.We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum.To improve this weakness we design a simple modification of the classic differential evolution algorithm.This modification limits the possible premature convergence to local minima and ensures the asymptotic global convergence.We also introduce concepts that are necessary for the subsequent proof of the asymptotic global convergence of the modified algorithm.We test the classic and modified algorithm by numerical experiments and compare the efficiency of finding the global minimum for both algorithms.The tests confirm that the modified algorithm is significantly more efficient with respect to the global convergence than the classic algorithm.

To reduce logistics scheduling costs and energy consumption, this paper studies the slab allocation and hot-rolling scheduling integrated optimization problem that arises in practical iron and steel enterprises. In this problem, slabs are first allocated to orders and then sent to heating furnaces for heating; then, they are sent to a hot-rolling mill for rolling. A 0–1 integer programming model is established to minimize the attribute difference in the allocation cost between slabs and orders, the switching cost of hot-rolling processing, and waiting times after slabs reach rolling mills. Given the problem’s characteristics, an improved differential evolution algorithm using a real-number coding method is designed to solve it. Three different heuristic algorithms are proposed to improve the quality of solutions in the initial population. Multiple parent individuals participate in the mutation operation, which increases the population diversity and prevents the algorithm from falling into the local optimum prematurely. Experiments on 14 sets of real production data from a large domestic iron and steel plant show that our improved differential evolution algorithm generates significantly better solutions in a reasonable amount of time compared with CPLEX, the simulated artificial method, and the classical differential evolution algorithm, and it can be used by practitioners.

Throughout the past few decades, a variant of differential evolution (DE) algorithms have been introduced with a competitive performance on complex optimization problems. However, the DE superiority is highly dependent on its control parameters and the search operators (i.e., mutation and crossover schemes). Therefore, to obtain the optimal performance, tuning the parameters is essential. In this paper, the DE algorithm is proposed that uses a new designed mutation scaling factor to dynamically adapt the movement of the individuals in the search space toward the optimal value during the evolutionary process. The numerical experiments are conducted on thirty CEC 2014 benchmark functions on four different dimensions; 10, 30, 50, and 100. The obtained results demonstrate that the proposed algorithm is highly competitive and shows better performance than the classical DE algorithm.

In this paper, a new control parameter adaptation scheme is introduced into the classical differential evolution (DE) algorithm. Then, a method for nonlinear system identification is proposed. The method combines modified differential evolution (MDE) and radial basis function (RBF) neural networks, which can auto-configure the structure of RBF networks and obtain the model parameters. The RBF network structure and parameters could be determined simultaneously based on input-output data without a priori knowledge. Finally, an example of nonlinear function identification is given to illustrate the effectiveness of the proposed approach.

Q-Learning-based parameter control in differential evolution for structural optimization

In this paper we proposed the circle trajectory assembly algorithm to control the multi-UAVs circular assembly formation. CTFAP solution provides rapid formation of UAVs on a circular orbit and solve the problem of large scattering distance. Proposed Distributed model prediction control framework improves the optimization ability and reduces the computation consumption with the better convergence ability of the UAV formation. Firstly, a circular trajectory following algorithm with an adaptive parameter is proposed to complete the rapid formation of UAVs on a circular orbit and solve the problem of large scattering distance during formation forming. Then, in the stage of formation reconfiguration, with distributed model prediction control framework (DMPC), the proposed method gets the prediction information of DMPC to optimize the population of classical differential evolution (DE) algorithm and improve the iterative optimization ability of DE algorithm. Experiments show that the proposed differential evolution algorithm greatly improves the efficiency of solving the formation reconfiguration problem under the DMPC framework and overcomes the disadvantages of random population of classical DE. For the proposed rapid forming method, assembly range is reduced by 41% compared with direct linearly formation assembly, and the formation forming time is reduced by approximately 21%. Compared with other optimization algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and DE, the proposed differential evolution algorithm reduces instruction response time of single-drones by 16%–30%.

Differential Evolution (DE) is an algorithm to solve possibly nonlinear and non-differentiable global optimization problems. Classical Differential Evolution (CDE) employs a synchronous generation-based evolution strategy. We propose a modification of the CDE algorithm by incorporating mutation, crossover and selection operations into an asynchronous strategy. A novel Asynchronous Differential Evolution (ADE) is well suited for parallel optimization. Moreover even in the sequential mode its rate of convergence is competitive to CDE. The performance of the Asynchronous Differential Evolution is reported on a set of benchmark functions.

Differential evolution (DE) is a powerful evolutionary algorithm for global optimization problems. Generally, appropriate mutation strategies and proper equilibrium between global exploration and local exploitation are significant to the performance of DE. From this consideration, in this paper, we present a novel DE variant, abbreviated to DMIE-DE, to further enhance the optimization capacity of DE by developing a dual mutations collaboration mechanism with elites guiding and inferiors eliminating techniques. More specifically, an explorative mutation strategy DE/current-to-embest with an elite individual serving as part of the difference vector and an exploitative mutation strategy DE/ebest-to-rand with selecting an elite individual as the base vector are employed simultaneously to achieve the balance between local and global performance of the whole population instead of only one mutation strategy in classical DE algorithm. The control parameters F and CR for above mutation strategies are updated adaptively to supplement the optimization ability of DMIE-DE based on a rational probability distribution model and the successful experience from the previous iterations. Moreover, an inferior solutions eliminating technique is embedded to enhance the convergence speed and compensate cost of the fitness evaluation times during the evaluation process. To evaluate the performance of DMIE-DE, experiments are conducted by comparing with five state-of-the-art DE variants on solving 29 test functions in CEC2017 benchmark set. The experimental results indicate that the performance of DMIE-DE is significantly better than, or at least comparable to the considered DE variants.

In this paper we present an empirical , comparative performance, analysis of fourteen variants of Differential Evolution (DE) and Multiple Trial Vectors Differential Evolution algorithms to solve unconstrained global optimization problems. The aim is (1) to compare Multiple Trial Vectors DE, which allows each parent vector in the population to generate more than one trial vector, against the classical DE and (2) to identify the competitive variants which perform reasonably well on problems with different features. The DE and Multiple Trial Vectors DE variants are benchmarked on 6 test functions grouped by features --- unimodal separable, unimodal nonseparable, multimodal separable and multimodal non-separable. The analysis identifies the competitive variants and shows that Multiple Trial Vectors DE compares well with the classical DE.

To enhance the optimization performance of differential evolution algorithm, by studying the implementation mechanism of differential evolution algorithm, a new idea of incorporating differential strategy and rotation of qubits in the Bloch sphere is proposed in this paper. In the proposed approach, the individuals are encoded by qubits described on Bloch sphere, and the rotation angles of qubits in current individual are obtained by differential strategy. The axis of rotation is designed by using vector product theory, and the rotation matrixes are constructed by using Pauli matrixes. Taking the corresponding qubits in current best individual as targets, the qubits in current individual are rotated to the target qubits about the rotation axis on the Bloch sphere. The Hadamard gates are used to mutate individuals. The simulation results of optimizing the minimum value of functions indicate that, for an iterative step, the average time of the proposed approach is 13 times as long as that of the classical differential evolution algorithm. When the same limited steps are applied in two approaches, the average optimization result of the proposed approach is 0.3 times as great as that of the classical differential evolution algorithm; when the same running time is applied in two approaches, the average optimization result of the proposed approach is 0.4 times as great as that of the classical differential evolution algorithm. These results suggest that the proposed approach is inefficient in computational ability; however, it is obviously efficient in optimization ability, and the overall optimization performance is better than that of the classical differential evolution algorithm.